In this problem we will be dealing with the probability density function (pdf) associated with a continuous random variable, X. Remember that the pdf is basically a function that assigns a probability density to the event of X taking a value x in the domain of X, with following two properties: 1 f(x) > 0, for all x
2 f(x) dx = 1.
f(x) does not give us the exact probability of X to take value x. Since the size of the domain of X is infinite, you cannot calculate the probability. Instead, you can calculate the probability of X to lie within a range:
Pr(a < X < b) = - / sa f(x) dx
Consider the following pdf function: 6x(1 – x) if 0 < x < 1,
f(x) = 0 otherwise. Calculate the probability of P(0.3 < X < 0.7)
a) 0.784
b) 0.568
c) 0.216
d) -0.568